I would suggest that you start with a reading of Plato's "Republic." Although there are no "kings" in the book, there is a great discussion of the role of the rulers (Guardians), their training, and their relationship to the people they "rule." I'm not sure that any real life king could do any of these things, or would even be interested in doing them, but your question asks for ideas.
Here's a place to start: http://www.enotes.com/plato
There is a problem in the nature of your question. What do you define as good? A fair king? A king who will be remembered? A king who was able to stay in power for a long time? Do you measure good by wealth of the country? By the abilty to maintain social order? By the one who has the most influence over domestic and international policies?
In becoming a good king....
well, kings are most often appointed by way of birth not of character. In other words, kings don't have to be good or bad to "become" king.